// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
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package com.google.ortools.sat.samples;

import com.google.ortools.Loader;
import com.google.ortools.sat.BoolVar;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.Literal;

/**
 * Reification is the action of associating a Boolean variable to a constraint. This boolean
 * enforces or prohibits the constraint according to the value the Boolean variable is fixed to.
 *
 * <p>Half-reification is defined as a simple implication: If the Boolean variable is true, then the
 * constraint holds, instead of an complete equivalence.
 *
 * <p>The SAT solver offers half-reification. To implement full reification, two half-reified
 * constraints must be used.
 */
public class ReifiedSampleSat {
  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    CpModel model = new CpModel();

    BoolVar x = model.newBoolVar("x");
    BoolVar y = model.newBoolVar("y");
    BoolVar b = model.newBoolVar("b");

    // Version 1: a half-reified boolean and.
    model.addBoolAnd(new Literal[] {x, y.not()}).onlyEnforceIf(b);

    // Version 2: implications.
    model.addImplication(b, x);
    model.addImplication(b, y.not());

    // Version 3: boolean or.
    model.addBoolOr(new Literal[] {b.not(), x});
    model.addBoolOr(new Literal[] {b.not(), y.not()});
  }
}
